Superconvergent HDG methods for linear elasticity with weakly symmetric stresses

We provide a systematic way of devising superconvergent mixed and hybridizable discontinuous Galerkin (HDG)methods for linear elasticity based on weak stress symmetry formulations. We show that, by suitably modifying the spaces defining superconvergent mixed and HDG methods for diffusion obtained in Cockburn et al. (Conditions for superconvergence of HDG methods for second-order elliptic problems, Math. Comp., 81, 1327-1353.), we obtain optimally convergent approximations for all unknowns, as well as a superconvergent approximation of the displacement. We use a projection-based a priori error analysis to achieve this goal.